Anyway let's take a look at the standard form of the equation of a hyperbola with a vertical transverse axis.

[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]

You've drawn one of the vertices at the origin, which is fine. But then you set [itex](h,k)=(0,0)[/itex] which is not fine. Those are the coordinates of the center, which certainly does not coincide with either of the vertices. You've also misidentified [itex]a[/itex] and [itex]b[/itex]. They are not the distances given in the problem.

Here's what I would do. Start from the diagram that you've drawn (with the vertex at the origin). That means that the center of the hyperbola is on the y-axis, which implies that [itex]h=0[/itex] in the above equation. Then use the 3 points on your diagram to find [itex]a[/itex], [itex]b[/itex], and [itex]k[/itex]. You have 3 points and you need to find 3 constants. That should be feasible.